International Journal of Science and Research (IJSR)
ISSN (Online): 2319-7064
Comparison between Genetic Algorithm based PID
Controller and Fuzzy Logic based PD Controller for
Position Control of DC Motor in Simulink
Laxmi Sahu1, Nivedita Singh2
1
M. Tech Scholar (D.E.), Electronics and Telecommunication
Rungta College of Engineering & Technology, Bhilai, C.G., India
2
Assistant Professor, Electronics and Telecommunication,
Rungta College of Engineering & Technology, Bhilai, C.G., India
Abstract: The objective of this paper is to compare the Genetic Algorithm based PID controller and Fuzzy Logic based PD controller
in position control system of a DC motor. Mainly there are two types of controller; PID and Fuzzy Logic PD controller will be used to
control the output response. The Fuzzy controller is used to control the position of a motor and motor parameters are taken from a
datasheet with respect to a real motor and a simulated model is developed using MATLAB Simulink Toolbox. The controlling signal is
computed in real time using suitable fuzzy membership functions depending upon the state of the power factor. It was found that the
proposed PD parameters adjustment by the Fuzzy Logic is better than the genetic algorithm method.
Keywords: Position control system, PID controller,PD controller, Fuzzy Logic controller,Genetic Algorithm, DC motor
1. Introduction
2. Mathematical Representation of a DC Motor
DC motor has excellent speed and position control
characteristics; hence it has been widely used in industry
even though its maintenance costs are higher than the
induction motor. As a result, position control of DC motor
has attracted considerable research and several methods
have evolved. Proportional-Integral Derivative (PID)
controllers have been widely used for speed and position
control of DC motor. The application of fuzzy logic is an
effective alternative for any problem where logical
inferences can be derived on the basis of causal relationships
7],[8]
Proportional-Integral-Derivative (PID) control is the most
common control algorithm used in industry and has been
universally accepted in industrial control. The PID controller
includes a proportional term, integral term and derivative
term, where the proportional term is to adjust the output of
controller according to all of the magnitude of error, the
integral term is used to remove the steady state error of
control system and improve the steady state response, the
derivative term is used to predict a trend of error and
improve the transient response of the system. A PID
controller improves the transient response of a system by
reducing the overshoot, and the settling time of a system [8]
Figure 1: DC Motor Model
In armature control of separately excited DC motors, the
voltage applied to the armature of the motor is adjusted
without changing the voltage applied to the field. Fig (1)
shows a separately excited DC motor equivalent model [7]
GA is a stochastic global adaptive search optimization
technique based on the mechanisms of natural selection.
Recently, GA has been recognized as an effective and
efficient technique to solve optimization problems,
compared with other optimization techniques. GA starts with
an initial population containing a number of chromosomes
where each one represents a solution of the problem which
performance is evaluated by a fitness function [11].
Paper ID: 020131408
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164
International Journal of Science and Research (IJSR)
ISSN (Online): 2319-7064
Let us combine the upper equations together:
Laplace transforms of (5) and (6) are:
If current is obtained from (8) and substituted in (7) we have
Then the relation between rotor shaft speed and applied
armature voltage is represented by transfer function:
The relation between position and speed is:
3. Proportional
Controller
Integral
Derivative
(PID)
PID controllers are widely used in industrial control
applications due to their simple structures, comprehensible
control algorithms and low costs. PID stands for
Proportional-Integral-Derivative. Each element of the PID
controller refers to a particular action taken on the error.
This section reviews the fundamental of PID controllers and
presents detailed simulations or design for development of
DC motor controller. PID controllers are commonly in the
time-domain behaviour of dynamic systems. They are
extremely popular because the controller provides good
response characteristics, which can be tuned using simple
rules and are easy to construct 9], [10]
Electric motor converts electrical energy into the mechanical
motion and are broadly classified into two different
categories: DC (Direct Current) motor and AC (Alternating
Current) motor. DC motors are usually modelled as linear
systems where linear control approaches are implemented.
Most of the linear controllers give unsatisfactory
performance due to the load changes of motor and due to the
nonlinearities of armature reaction. The impact of external
disturbances and of nonlinearities may risk the stability of
the closed loop system. Fig (3) shows the schematic model
of a control system with a PID controller 10]
Then the transfer functions between shaft position and
armature voltage at no-load is:
Fig (2) shows the DC motor model built in Simulink. Motor
model was converted to a 2-in 2-out subsystem. Input ports
are armature voltage (Va) and load torque (Tload) and the
output ports are angular speed in (w) and position (teta).
Figure 3: PID control system
Control signal is u (t) a linear combination of error e (t), its
integral and derivative.
Figure 2: Simulink Model for DC Motor
A 3.70 kW, 240V, 1750 rpm DC motor with the below
parameters was used:
4. Fuzzy Logic
Fuzzy logic is a derivative from classical Boolean logic and
implements soft linguistic on a continuous range of truth
values to be defined between conventional binary. It can
often be considered a suspect of conventional set theory.
Since fuzzy logic handles approximate information in a
systematic manner, it is ideal for controlling non-liner
systems and fro modelling complex systems where an
Paper ID: 020131408
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International Journal of Science and Research (IJSR)
ISSN (Online): 2319-7064
inexact model exists or systems where ambiguity or
vagueness is common. A typical fuzzy system consists of a
rule base, membership functions and an inference procedure
[9]. Today, fuzzy logic are found in a variety of control
applications like chemical process control, manufacturing
and in such consumer products as washing machines, video
cameras and automobiles. Fuzzy logic is a suspect of
conventional Boolean logic that has been extended to handle
the concept of partial truth- truth- values between
“completely true” and “completely false”. Fuzzy theory as a
single theory, we should regard the process of fuzzification
as a methodology to generalize ANY specific theory from a
crisp (discrete) to a fuzzy (continuous) form. Thus, recently,
researchers have also introduced “fuzzy calculus” and
“fuzzy differential equations” [2], [3].
4.1. Fuzzy Rule Base
Fuzzy logic has been centered on the point that it makes use
of linguistic variables as its rule base. If a variable can take
words in natural language as its values, it is called linguistic
variable, where the words are characterized by fuzzy sets
defined in the universe of discourse in which the variable is
defined. Examples of these linguistic variables are slow,
medium, high, young and thin. There could be combinations
of this variable too, like “slow-young horse”, “a thin young
female.” These characteristics are termed atomic terms while
their combinations are called compounded terms. In the real
world, words are often used to describe characteristics rather
than numerical values. For example, one would say “the car
was going at 100 miles per hour.” Terms such as slightly,
very, more or less, etc. are called linguistic hedges since
they add extra description to the variables, i.e. very – slow,
more or less, slightly high, etc. At the heart of the fuzzy rule
base are the IF-THEN rules 5], [6]
control rules based on the inputs. The precise fuzzy
membership functions depend on the wide range of inputs
and the general response characteristics of the system.
Within power systems, fuzzy logic controllers primarily
using MATLAB – FIS Editor have been proposed. The
structure of the Fuzzy Logic Controller (FLC) and its design
consist of the following steps:
1) Identification of input and output variables.
2) Construction of control rules.
3) Establishing the approach for describing system state in
terms of fuzzy sets, i.e., establishing fuzzification method
and fuzzy membership functions.
4) Selection of the compositional rule of the inference.
4.3. Membership Functions
The membership functions consist of the seven linguistic
terms:
* Negative Large Large (NLL)
* Negative Large (NL)
* Negative Small (NS)
* Zero (Z)
* Positive Small (PS)
* Positive Large (PL)
* Positive Large Large (PLL)
The input e presented in Fig (6) consists of all seven terms to
increase response with respect to the error. The input ce and
output cu both have five terms as shown in Fig (7) and Fig
(8) since it was optimal to keep them at a lower degree of
precision. All membership functions were chosen to be of
the triangular and trapezoidal type, mostly due to its
common use during class and straightforward
implementation.
A fuzzy IF-THEN rule is expressed as,
IF<fuzzy proposition>,
THEN <fuzzy proposition>
Propositions are linguistic variables or atomic terms as
described previously. This type of rule based system is
different from the classical expert systems, In that, rules may
not necessarily be derived from human expertise; they may
also be derived from other sources. Three types of linguistic
variable forms exist.
Figure 6: Membership function for e, μe(x1)
1. Assignment statements
2. Conditional statements
3. Unconditional statements
4.2. Fuzzy Logic Controller Design
The traditional control design paradigm is to form a system
model and develop control laws. The controller may be
modified based on results of testing and experience. Due to
difficulties of analysis, many such controllers are linear. The
fuzzy controller approach should be reversed to some extent.
General control rules will be based on experience are
introduced and analyzed. Implementation of this concept is
for anticipating the position and reducing the control level to
avoid overshoot. The quantities like “small” and “large” are
used in fuzzy quantities. A controller design requires a set of
Paper ID: 020131408
Figure 7: Membership function for ce, μce(x2)
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166
International Journal of Science and Research (IJSR)
ISSN (Online): 2319-7064
5. Tuning of PID Controller Using Genetic
Algorithm Approach
5.1 Overview of Genetic Algorithm
Figure 8: Membership function for cu, μcu(y)
4.4. Membership Rule Base
The input e uses seven membership functions, while ce uses
five, which required a rule base consisting of 35(7x5) rules.
The resulting rule base can be seen in Table 1. The rule base
was developed to present smooth, gradual transitions to an
error relative to zero error by attempting to decrease the
change in error, ce.
GA is a stochastic global adaptive search optimization
technique based on the mechanisms of natural selection.
Recently, GA has been recognized as an effective and
efficient technique to solve optimization problems,
compared with other optimization techniques. GA starts with
an initial population containing a number of chromosomes
where each one represents a solution of the problem which
performance is evaluated by a fitness function.
Basically, GA consists of three main stages: Selection,
Crossover and Mutation. The application of these three basic
operations allows the creation of new individuals which may
be better than their parents. This algorithm is repeated for
many generations and finally stops when reaching
individuals that represent the optimum solution to the
problem. The GA architecture is shown in Fig (11).
Table 1: Membership Rule Base
Figure 9: Response of the system based on the fuzzy logic
controller.
4.5. FPD controller design
Fig (10) shows the control system with an FPD
controller
Figure 11: Genetic Algorithm Architecture
5.2 Implementation of GA based PID controller
GA can be applied to the tuning of PID position controller gains
to ensure optimal control performance at nominal operating
conditions. The block diagram GA-PID controller system is
given below and also the genetic algorithm parameters chosen
for the tuning purpose are shown below,
Figure 10: Control system with an FPD controller
Paper ID: 020131408
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167
International Journal of Science and Research (IJSR)
ISSN (Online): 2319-7064
Figure 12: Structure of GA-PID controller
6. Conclusion
The results of experiments on FPD & GA PID model revels that
the controller designed with FPD has much faster response than
the response of GA PID controller .The Fuzzy Logic designed
PD is much better than the GA PID in terms of the rise time and
the settling time. Also fuzzy logic controller is able to
sensitiveness to the variation of the reference position compared
to GA PID. Moreover the FPD is very easy to implement as it is
designed only based on the input & output of the plant and does
not required a mathematical model of the plant as in case of GA
PID. The comparison of both the Fuzzy based controller and
PID controller on a DC motor,” Procee. of IEEE (FOCI
2007), pp. 531-538, 2007.
[8] G. Haung and S. Lee, “PC based PID speed control in
DC motor,” IEEE Conf. SALIP-2008, pp. 400- 408,
2008.
[9] Zadeh, M. H., Yazdian, A. and Mohamadian, M.,
Robust Position Control in DC Motor by Fuzzy Sliding
Mode Control. International Symposium on Power
Electronics, Electrical Drives, Automation and Motion
(SPEEDAM 2006), 1413-1418, 2006.
[10] G. Haung and S. Lee, “PC based PID speed control in
DC motor,” IEEE Conf. SALIP-2008, pp. 400- 408,
2008.
[11] Petr Kejík, Stanislav Hanus “Comparison of Fuzzy
Logic and Genetic Algorithm Based Admission Control
Strategies for UMTS System” Dept. of Radio
Electronics, Brno University of Technology, Purkyňova
118, 612 00 Brno, Czech Republic,pp.6-10, VOL. 19,
NO. 1, APRIL 2010.
GA based controller meets to the conclusion that fuzzy
based controller (FPD) has the optimized performance
compared to the genetic based controller (GA PID).
7. Acknowledgment
Here we would like to acknowledge all the people associated
with this project that has helped in one or the other manner
towards the completion of the project. I also like to thank to
my guide who has helped me in this project. I also
acknowledge my friends and family members.
References
[1] J. Jantzen, "Tutorial on Fuzzy Logic", Technical
University of Denmark: Department of Automation,
Technical report number 98-E 868, 19 Aug 1998.
[2] J. Jantzen, "Design of Fuzzy Controllers", Technical
University of Denmark: Department of Automation,
Technical report number 98-E 864, 19 Aug 1998.
[3] C. C. Lee, "Fuzzy Logic in Control Systems: Fuzzy
Logic Controller-Part I", IEEE Transactions on
Systems, Man, and Cybernetics, Vol. 20, No. 2, pp.
404-418, 1990.
[4] C. C. Lee, "Fuzzy Logic in Control Systems: Fuzzy
Logic Controller-Part II", IEEE Transactions on
Systems, Man, and Cybernetics, Vol. 20, No. 2, pp.
419-435, 1990.
[5] R. Isermann, "On Fuzzy Logic Applications for
Automatic Control, Supervision, and Fault Diagnosis",
IEEE Transactions on Systems, Man, and Cybernetics
Part A: Systems and Humans, Vol. SMC-28, No. 2, pp.
221-235, 1998.
[6] R. R. Yager and D. P. Filev, "Essentials of Fuzzy
Modeling and Control", John Wiley & Sons, 1994.
[7] O. Montiel, R. Sepúlveda, P. Melin and O. Castillo,
“Performance of a simple tuned Fuzzy controller and a
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